I decided to send blizzard an email just to get a confirmation from them. Here's what I emailed them.
"Hey there! I didn't know where to put this, but I was wondering about the early access for Demon Hunters.
Are they going to be able to do the Broken shore questline and the invasion quests around the world?"
and the respond
"This is Game Master Ezlyniel. Thank you very much for contacting us today regarding your queries about the Demon Hunters.
You cannot imagine how much I understand you. I really want to play them as much as I can and try the Demon Hunter tank and of course, the Dark Shore questline.
Everyone who pre-purchased the expansion Legion will have early access to the Demon Hunter. That means, that you will be able to do the Broken Shore questline and the invasion quests around the world.
This will happen when the pre-patch release! You can actually find all the information in the following link:
http://eu.battle.net/wow/en/blog/201...ere-08-07-2016
We only have to wait a little bit more. The Legion is almost here!
Have a great day!"
I guess the "Dark Shore questline" is a typo ^^